Cluster free energy in the simple-cubic Ising model

The Monte Carlo technique previously developed to compute directly the free-energy difference between two clusters containing $N+1$ and N particles is applied to the three-dimensional cubic Ising model with nearest-neighbor interactions. For cluster sizes 1≤N≤19, at two reduced temperatures (TTc=0.4 and 0.59) it is found that down to surprisingly small sizes (N≥8) the free energy FN can be written as FN=Na+N2/3b+N1/3c+d+τβ^-1lnN, where a and τ are given their theoretical value for bulk phases, and b, c, and d can be understood, respectively, as the surface contribution, a step contribution, and a vertex contribution. A Fisher-type model (FN=Na+N^σΣ+τβ^-1lnN) when fitted to the data yields a size- and temperature-dependent value of σ. Other proposed models are shown to depart systematically from our data. Typical values of nucleation rates for this model, as predicted from the present data, range from 10^-3 to 10⁺²---those expected from the classical capillarity approximation of FN.